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papers

Publications (163)

math.CO2013

Extremal results in sparse pseudorandom graphs

David Conlon, Jacob Fox, Yufei Zhao

SzemerÃ©di's regularity lemma is a fundamental tool in extremal combinatorics. However, the original version is only helpful in studying dense graphs. In the 1990s, Kohayakawa and…

math.CO2010

Crossings, colorings, and cliques

Michael O. Albertson, Daniel W. Cranston, Jacob Fox

Albertson conjectured that if graph $G$ has chromatic number $r$ , then the crossing number of $G$ is at least that of the complete graph $K_{r}$ . This conjecture in the case $r = 5$ is…

math.CO2025

A question of ErdÅs and Graham on Egyptian fractions

David Conlon, Jacob Fox, Xiaoyu He +4

Answering a question of ErdÅs and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive int…

math.CO2014

The ErdÅs-GyÃ¡rfÃ¡s problem on generalized Ramsey numbers

David Conlon, Jacob Fox, Choongbum Lee +1

Fix positive integers $p$ and $q$ with $2 \leq q \leq (2 p)$ . An edge-coloring of the complete graph $K_{n}$ is said to be a $(p, q)$ -coloring if every $K_{p}$ receives at leas…

math.CO2022

Quasiplanar Graphs, String Graphs, and the Erdos-Gallai Problem

Jacob Fox, Janos Pach, Andrew Suk

An $r$ -quasiplanar graph is a graph drawn in the plane with no $r$ pairwise crossing edges. Let $s \geq 3$ be an integer and $r = 2^{s}$ . We prove that there is a constant $C$ such tha…

math.CO2019

Bounded VC-dimension implies the Schur-Erdos conjecture